Let $K$ be a finite extension of $\Q_p$, and $K^{un}$ its unramified subfield. The **unramified degree** of $K$ is the degree $[K^{un}:\Q_p]$, which is equal to its residue field degree.

Since $\Q_p$ has a unique unramified extension of degree $n$ for each positive integer $n$, the unramified degree of an extension determines its unramified subfield.

The **Galois unramified degree** of $K$ is the unramified degree of its Galois closure.

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- Review status: reviewed
- Last edited by Andrew Sutherland on 2021-05-14 21:30:55

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- 2021-05-14 21:30:55 by Andrew Sutherland (Reviewed)
- 2021-05-14 21:27:56 by Andrew Sutherland
- 2021-05-14 16:53:53 by John Jones (Reviewed)
- 2021-05-14 16:32:13 by Jakob de Raaij
- 2018-07-04 23:31:23 by John Jones (Reviewed)

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